Tag Archives: science

Bringing Harmony to the Global Warming Debate

For some time now, our regular contributor James Glover been promising me a post with some statistical analysis of historical global temperatures. To many the science of climate change seems inaccessible and the “debate” about climate change can appear to come down to whether you believe a very large group of scientists or a much smaller group of scientists people. Now, with some help from James and a beer coaster, you can form your own view.

How I wish that the title of this article was literally true and not just a play on words relating to the Harmonic Series. Sadly, the naysayers are unlikely to be swayed, but read this post and you too can disprove global warming denialism on the back of a beer coaster!

It is true, I have been promising the Mule a statistical analysis of Global Warming. Not only did I go back and look at the original temperature data but I even downloaded the data and recreated the original “hockey stick” graph. For most people the maths is quite complicated though no more than an undergraduate in statistics would understand. It all works out. As a sort of professional statistician, who believes in Global Warming and Climate Change, I can only reiterate my personal  mantra: there is no joy in being found to be right on global warming.

But before I get onto the beer coaster let me give a very simple explanation for global warming and why the rise in CO2 causes it. Suppose I take two sealed glass boxes. They are identical apart from the fact that one has a higher concentration of CO2. I place them in my garden (let’s call them “greenhouses”) and measure their temperature, under identical conditions of weather and sunshine, over a year. Then the one with more CO2 will have a higher temperature than the one with less. Every day. Why? Well it’s simple: while CO2 is, to us, an “odourless, colourless gas” this is only true in the visible light spectrum. In the infra-red spectrum, the one with more CO2 will be darker. This means it absorbs more infrared radiation and hence has a higher temperature. CO2 is invisible to visible light but, on it’s own, would appear black to infrared radiation.  The same phenomenon explains why black car will heat up more in the sun than a white one. This is basic physics and thermodynamics that was understood in the 19th century when it was discovered that “heat” and “light” were part of the same phenomenon, i.e. electromagnetic radiation.

So why is global warming controversial? Well, while what I said is undeniably true in a pair of simple glass boxes, the earth is more complicated than these boxes. Radiation does not just pass through, it is absorbed, reflected and re-radiated. Still, if it absorbs more radiation than it receives then the temperature will increase. It is not so much the surface temperature itself which causes a problem, but the additional energy that is retained in the climate system. Average global temperatures are just a simple way of trying to measure the overall energy change in the system.

If I covered the glass box containing more CO2 with enough aluminium foil, much of the sunshine would be reflected and it would have a lower temperature than its lower CO2 twin. Something similar happens in the atmosphere. Increasing temperature leads to more water vapour and more clouds. Clouds reflect sunshine and hence there is less radiation to be absorbed by the lower atmosphere and oceans. It’s called a negative feedback system. Maybe that’s enough to prevent global warming? Maybe, clouds are very difficult to model in climate models, and water vapour is itself a greenhouse gas. Increasing temperature also decreases ice at the poles. Less ice (observed) leads to less radiation reflected and more energy absorbed. A positive feedback. It would require a very fine tuning though for the radiation reflected back by increased clouds to exactly counteract the increased absorption of energy due to higher CO2. Possible, but unlikely. Recent models show that CO2 wins out in the end. As I as said, there is no joy to being found right on global warming.

So enough of all that. Make up your own mind. Almost time for the Harmony. Perusing the comments of a recent article on the alleged (and not actually real) “pause” in global warming I came across a comment to the effect that “if you measure enough temperature and rainfall records then somewhere there is bound to be a new record each year”. I am surprised they didn’t invoke the “Law of Large Numbers” which this sort of argument usually does. Actually The Law of Large Numbers is something entirely different, but whatever. So I asked myself, beer coaster and quill at hand, what is the probability that the latest temperature or rainfall is the highest since 1880, or any other year for that matter?

Firstly, you can’t prove anything using statistics. I can toss a coin 100 times and get 100 heads and it doesn’t prove it isn’t a fair coin. Basically we cannot know all the possible set ups for this experiment. Maybe it is a fair coin but a clever laser device adjusts its trajectory each time so it always lands on heads. Maybe aliens are freezing time and reversing the coin if it shows up tails so I only think it landed heads. Can you assign probabilities to these possibilities? I can’t.

All I can do is start with a hypothesis that the coin is fair (equal chance of heads or tails) and ask what is the probability that, despite this, I observed 100 heads in a row. The answer is not zero! It is actually about 10-30. That’s 1 over a big number: 1 followed by 30 zeros. I am pretty sure, but not certain, that it is not a fair coin. But maybe I don’t need to be certain. I might want to put a bet on the next toss being a head. So I pick a small number, say 1%, and say if I think the chance of 100 head is less than 1% then I will put on the bet on the next toss being heads. After 100 tosses the hypothetical probability (if it was a fair coin) is much less than my go-make-a-bet threshold of 1%. I decide to put on the bet. It may then transpire that the aliens watching me bet and controlling the coin, decide to teach me a lesson in statistical hubris and make the next toss tails and I lose. Unlikely, but possible. Statistics doesn’t prove anything. In statistical parlance the “fair coin” hypothesis is called the “Null Hypothesis” and the go-make-a-bet threshold of 1% is called the “Confidence Level”.

Harmony. Almost. What is the probability that if I had a time series (of say global temperature since 1880) that the latest temperature is a new record. For example the average temperature in Australia in 2013 was a new record. The last average global temperature record was in 1998. I think it is trending upwards over time with some randomness attached. But there are all sort of random process which produce trends, some of which are equally likely to have produced a downward trending temperature graph. All I can really do, statistically speaking, is come up with a Null Hypothesis. In this case my Null Hypothesis is that the temperature doesn’t have a trend but is just the result of random chance. There are various technical measures to analyse this, but I have come up with one you can fit on the back of a beer coaster.

So my question is this: if the temperature readings are just i.i.d. random processes (i.i.d. stands for “independent and identically distributed”) and I have taken 134 of these (global temperature measurements 1880-2014) what is the probability the latest one is the maximum of them all? It turns out to be surprisingly easy to answer. If I have 134 random numbers then one of them must be the maximum. Obviously. Since they are iid I have no reason to believe it will be the first, second, third,…, or 134th. It is equally likely to be any one of those 134. So the probability that the 134th is the maximum is 1/134 = 0.75% (as it is equally likely that, say, the 42nd is the maximum). If I have T measurements then the probability that the latest is the maximum is 1/T. So when you hear that the latest global temperature is a maximum, and you don’t believe in global warming, then be surprised. As a corollary if someone says there hasn’t been a new maximum since 1998 then the probability of this still being true, 14 years later, is 1/14 = 7%.

So how many record years do we expect to have seen since 1880? Easy. Just add up the probability of the maximum (up to that point) having occurred in each year since 1880. So that would be H(T) = 1 + 1/2 + 1/3 + … + 1/T. This is known as the Harmonic Series. It is famous in mathematics because it almost, but doesn’t quite converge. For our purposes it can be well approximated by H(T) =0.5772+ ln(T) where ln is the natural logarithm, and 0.5772 is known as the Euler-Mascharoni constant.

So for T=134 we get from this simple beer-coaster sized formula: H(134) = 0.5772+ln(134)= 5.47. (You can calculate this by typing “0.5772+ln(134)” into your Google search box if you don’t have a scientific calculator to hand). In beer coaster terms 5.47 is approximately 6. So, given the Null Hypothesis (which is that there has been no statistically significant upward trend since 1880) how many record breaking years do we expect to have seen? Answer: less than 6. How many have we seen: 22. 

Temperature peaks

Global temperatures* – labelled with successive peaks

If I was a betting man I would bet on global warming. But there will be no joy in being proven right.

James rightly points out that the figure of 22 peak temperatures is well above the 6 you would expect to see under the Null Hypothesis. But just how unlikely is that high number? And, what would the numbers look like if we took a different Null Hypothesis such as a random walk? That will be the topic of another post, coming soon to the Stubborn Mule!

* The global temperature “anomaly” represents the difference between observed temperatures and the average annual temperature between 1971 and 2000. Source: the National Climate Data Center (NCDC) of the National Oceanic and Atmospheric Administration (NOAA).

John Graunt and the Birth of Medical Statistics

Dr John Carmody of the Department of Physiology at the University of Sydney, recently appeared on the ABC Radio National program, Occams Razor, speaking about John Graunt, a man many years ahead of his time. For those of you preferring the written to the auditory format, he has kindly provided his talk as a guest post for the Mule.

We become blind to what is familiar.

So dependent is modern medicine on accurate measurement that patients and doctors alike accept the fact without surprise or question, perhaps believing that it is inevitable. Yet the importance of numbers of any sort in medicine, let alone precise ones, is a concept that is little over 350 years old. In physiology, the most basic of medical sciences, this dates only from 1628 when William Harvey published his great book on the circulation, a discovery which he formulated and proved through numerical argument.

Then in London, in 1662, 350 years ago this year, John Graunt published a booklet which we can now understand was the beginning of medical statistics, of epidemiology, of medical demography. In the manner of those times he gave it the formidable title of Natural and political observations, mentioned in a following Index, and made upon the Bills of Mortality, to which he added the supplementary description, “With reference to the Government, Religion, Trade, Growth, Air, Diseases and the several changes of the said City”. His work was, therefore, far wider than establishing a new medical discipline. He was arguing for the necessary interaction of medicine, good government and sensible policy—indeed, perhaps for the discipline of quantitative economics, as well. We can realize how original Graunt’s work was when we remember that the only previous English census was the compilation of the “Domesday Book” in 1086 and that the first official census was not taken until 1801.

Graunt’s genius was to recognize—as none of his contemporaries had done—the immense importance of what we would now call a “database” which had existed in London for about 60 years. These were the so-called “Bills of Mortality” which the administrative clerks of the Church of England parishes in London had been obliged to keep scrupulously since James I became king in 1603. In fact, when James granted a charter to the Company of Parish Clerks in 1611, he legally obliged the members to be far more diligent in their recording than before his accession to the throne. These Bills recorded the christenings and the burials, parish by parish, each week. As well, the burials were accompanied by what Graunt called the “diseases and casualties” which brought about those deaths. He drew on the records of about 97 parishes within the city walls and 16 outside them and in a typical year he would have to deal with 20,000-25,000 burials and supposed causes of death.

He was very concerned with the reliability of those diagnoses which were rarely professionally reported. As he wrote, “When anyone dies, then, either by tolling, or ringing of a Bell, or by bespeaking of a Grave of the Sexton, the same is known to the Searchers corresponding with the said Sexton. The Searchers hereupon (who are ancient matrons, sworn to their office), repair to the place where the dead Corps lies, and by view of the same, and by other enquiries, they examine by what disease or casualty the corps died. Hereupon, they make their report to the Parish-Clerk.” Graunt keenly recognized the flaws in such a system and acknowledged that “I have heard some candid physicians complain of the darkness, which they themselves were in hereupon”. He also saw the possibility of corruption, the temptation, as he put it, for “the old-women searchers after the mist of a cup of ale and the bribe of a two-groat fee” to report, say, “Consumption” instead of the more shaming “infection of the spermatick parts”. In fact, he was convinced that syphilis, or the “French pox” was substantially under-reported.

Nevertheless, he decided that the incidence of such problems probably had changed little over the period which he was examining, so errors of those kinds were likely to be fairly consistent. “The ignorance of the Searchers is no impediment to the keeping of sufficient and usefull Accompts”. However, he saw other potential flaws in his data. Whereas corpses had to be disposed of for obvious reasons of health and amenity, and therefore burials provided a pretty reliable index of deaths, christenings did not reliably count births. This was because Catholics and Puritans, in particular, were reluctant to have their offspring baptized into a faith which they opposed. Furthermore, from 1649, when Charles I was executed, until 1660, when his son was restored to the Throne, the government of England was dominated by the Puritans, so many people were more confident to flout Anglican authority. Graunt was therefore obliged to make some corrections to his figures. Then, in attempting to make comparisons of births, deaths and diseases between London and the country, he had to deal with population disparities and calculate per capita rates in the absence of any census information. Another source of error, which was especially nettlesome during outbreaks of plague, was under-reporting of that disease—either because the affected households simply threw bodies into the streets, or because the “Searchers” were unwilling to inspect the bodies closely for fear of contracting the disease themselves. This meant, as Graunt recognized, that plague deaths were under-reported and the counts attributed to other causes were inflated.

Not content with simply aggregating and analyzing his data, Graunt drew up a synoptic list of 106 points in what he called his “Index”, several of which were recommendations for social and health policy.

He asserted, for example, that it would be “better to maintain all Beggars at the publick charge, though earning nothing, then to let them beg about the streets; and that employing them without discretion, may do more harm, than good”. He also found that “not one in two thousand are murthered in London”—a statistical finding which could be considered the birth of serious criminology. Even more importantly, he found that “the Rickets is a new disease, both as to name, and thing”. That diagnosis, he realized, did not appear at all in the Bills until 1634 and even then there were only 14 cases in that year; but by 1658 there were 476 cases. He seriously considered the possibility that previously it had been misdiagnosed but used his data to disprove that hypothesis. This is a remarkable reflection of the approach of William Harvey who had also used numbers to falsify arguments against his concept of the circulation of the blood.

Three years later, at the end of 1665, Graunt published, London’s dreadful visitation, or, A collection of all the Bills of Mortality for this present year, in which he applied the same analytical techniques to the demographic consequences of the “Great Plague of London”. Even today it is amazing and chilling reading: week by week, parish by parish, it documents the relentless surge of that awful disease from its first real appearance in May when 28 cases were recorded. Thereafter, the fatalities increased horrifyingly: about 340 in June; 4400 in July; 13,000 in August; 32,300 in September; 13,300 in October; 4,100 in November and 1,060 in December—a recorded total for that year of 68,600 deaths. And remember: in his earlier book, Graunt had decided that plague was, in such circumstances, seriously under-reported.

Its effects can be put into perspective by this contrast. For example, in the week from 29 August to 5 September, the Bills of Mortality reported 6,988 deaths from plague out of 8,252 burials recorded in the London parishes for that week, and in those 7 days a mere 167 christenings were recorded. Altogether, there were 9,967 christenings in that year and 97,306 burials—an almost 10-fold difference compared with the more usual disparity of less than two-fold and, according to Graunt’s estimates, those burials represented more than 22% of the population of London.

This catastrophic effect on the population of the capital could hardly be replenished by the usual birthrate because even in the first part of 1665 the christenings had been only 57% of the number of burials. In his earlier book, though, Graunt had found that there was substantial nett loss of population from the country to London. The result was that by 1675 the population of the capital was back to pre-plague levels.

In 1663, between the publication of Graunt’s extraordinary books, he had been elected as a Fellow of the Royal Society of London, though this seems not to have been an entirely straightforward matter. By profession, this genius was a haberdasher, whereas, according to the first history of the Royal Society, its membership was comprised principally of “gentlemen, free, and unconfin’d”. That self-congratulatory but diplomatic history which Thomas Sprat published in 1667, only 6 years after King Charles II had joined the society, says of Graunt’s election, “it is the recommendation which the King himself was pleased to make” adding that “his Majesty gave this particular charge to His Society, that if they found any more such Tradesmen, they should be sure to admit them all, without any more ado”. Those last words suggest to me that the “Gentlemen” of the Society required a little Royal “persuasion” which, the King seemed to be hinting, he did not wish to exert a second time.

Graunt was moderately active in the affairs of the Royal Society for a few years, but in the late 1660s he fell onto hard financial times, principally, I think, on account of his conversion to Catholicism. Certainly, this required him to relinquish his military commission as a Major and doubtless had adverse effects on his professional activities. He was eventually bankrupted and died in 1674.

His fading fame was not the only thing which then disappeared. So did some important records of the Worshipful Company of Parish Clerks. In his History of London, William Maitland noted, in 1739, that he had access to the Bills of Mortality only from 1664, stating that the Company “were of the opinion that the same was lent to Graunt…..but by some accident never returned”. He was neither the first nor the last scholar to forget to return borrowed materials to their owners. Nevertheless, the world of medicine remains forever in his debt. Graunt taught doctors that, for all of the importance of their focus on each individual patient, they must also shift their attention to understand what is happening to the whole population and to do so with the aid of the best possible statistics. The world is also in debt to King James, not only for the Bible which he commissioned, but for his insistence that the Parish Clerks should keep those good statistics. It is an unusual example of a beneficial combination of science and religion.

Holiday reading

My now traditional annual pilgrimage to the South coast of New South Wales saw the rainiest weather I can remember. While it was nothing on the scale seen in Queensland and Victoria over recent weeks, it did take its toll on some of the wildlife: we saw dozens of dead porcupine puffers washed up on the beach, apparently the victims of an algal bloom triggered by the rains. On the plus side, the lack of sunshine did help me to catch up on a bit of overdue reading, including a review copy of a Beginner’s Guide to R which you can expect to hear more about when I manage to finish writing the review.

I also read two books about climate change, which were very different in style and content.

Merchants of Doubt

The first was Erik Conway and Naomi Oreskes’ Merchants of Doubt (How a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Global Warming). The book is not really about climate change per se, but rather the modus operandi of a number of key climate skeptics. In the process it sheds some interesting light on a question I considered here on the blog about a year ago: why does belief or disbelief in the reality of climate change tend to be polarised along political lines? Most of the protagonists in the Merchants of Doubt are scientists, many of whom were physicists involved in the original US nuclear weapons program. The thesis that Conway and Oreskes build is that these scientists were committed anti-Communists and as the Cold War began to thaw, they saw threats to freedom and capitalism in other places, particularly in the environmental movement. That, at least, is the explanation given as to why the same names appear in defence of Ronald Reagan’s “Star Wars” missile defence scheme, in defence of the tobacco industry (first arguing against claims about the health risks of smoking, later about the health risks of second-hand smoke), dismissing the idea of acid rain and finally casting doubt on claims of human-induced climate change.

While I would not expect the book to sway any climate change skeptic, it should at least encourage people to think a bit harder about messengers as well as the message. It certainly prompted me to do just that. When reading the chapter on the second-hand smoke controversy, I immediately thought of an episode of the Penn and Teller’s very entertaining pseudo-science debunking TV series Bullshit*. The episode in question, as I remembered it, did a convincing job of portraying the risks of second-hand smoke (SHS) as dubious at best. Watching it again was eye-opening. Looking past the scathing treatment of the anti-SHS activist, I focused instead on the credentials of the talking heads who were arguing that the science was not settled. The two main experts were Bob Levy from the Cato Institute, a libertarian think-tank, and Dr Elizabeth Whelan, the president of the American Council on Health and Science.

Levy’s voice immediately suggests he is a smoker, which does not, of course, disqualify him from questioning the science of SHS. More intriguing is the fact that the Cato Institute regularly appears as a company of interest in the Merchants of Doubt. Conway and Oreskes draw a number of links between the Cato Institute and both the defence of the tobacco industry and skepticism of global warming, particularly in the person of Steven Milloy who, before joining Cato, worked for a firm whose main claim to fame was to provide lobbying and public-relations support for tobacco giant Phillip Morris.

As for the American Council on Health and Science, it sounds at first like some kind of association of health professionals (which is presumably why Warren chose the name). It is in fact an industry-funded lobby group…sorry, I mean an independent, nonprofit, tax-exempt organisation. Exactly how much of their funding comes from where is now shrouded in mystery, but here are the details as of 1991.

Of course, scrutinising the backgrounds Levy and Whelan does not prove that their claims are wrong. It does, however, raise the question of why Penn and Teller did not interview anyone more independent, perhaps even a scientist, who expressed the same doubts.

What’s the Worst That Could Happen?

The second book on climate change that the rain helped me to read was Greg Craven’s book What’s the Worst That Could Happen?. I bought this after watching Craven’s amusing, if flawed, video “The Most Terrifying Video You Will Ever See”. Craven, a high-school science teacher in Oregon, has clearly workshopped the issue of climate change extensively with his students and the insight he wants to share in his videos and his book is essentially that the whole problem can be viewed from a game-theoretic perspective. Rather than trying to decide what is true or not (are the skeptics right or are the warmers right?), the important question is should we be acting or not.

Craven decision gridCraven’s Global Warming Decision Grid

In his video, Craven uses an action versus outcome “decision grid” to argue that the consequences of not acting in the event that global warming turns out to be true are worse than the consequences of acting (i.e. economic costs) if it turns out to be false. The argument is entertaining, but unfortunately flawed. The problem is that it can be applied to any risk, however remote. As he writes in the book:

Simply insert any wildly speculative and really dangerous-sounding threat into the grid in place of global warming, and you’ll see the grid comes to the same conclusion–that we should do everything possible to stop the threat. Even if it’s something like giant mutant space hamsters (GMSHs).

The book is an attempt to rescue his idea by developing a series of tools to help sift through the arguments for and against climate change without having to actually understand the science. Along the way, he includes an extensive discussion of confirmation bias which I enjoyed as I am fascinated by cognitive biases. Ultimately though, his conclusions rest on an argument from authority. While he makes an excellent case for the important role that authority plays in science, this approach will not win over the skeptics I know: I can already hear their riposte in the form of the establishment’s rejection of Albert Wegener’s theory of continental drift.

Skeptics aside, What’s the Worst That Could Happen? is an extremely accessible book (perhaps even too folksy in its style for some) and is probably best read by those who are not already entrenched in one camp or another and are just sick of the whole shouting match.

* Long-time readers may remember that Bullshit has been mentioned on the blog before in this post about bottled water.

Vale Martin Gardner

I was saddened to hear today that Martin Gardner has passed away at the age of 95. Born in 1914, Gardner was a prolific and gifted writer. He is best known for his mathematical and scientific writing, but he also dabbled in magic and philosophy. His The Annoted Alice is perhaps the ultimate edition of Lewis Carrol’s Alice in Wonderland.

For many years he wrote a column on “Mathematical Recreations” in Scientific American, which I read avidly as a child. These columns gave me endless pleasure, solving puzzles, constructing tetraflexagons and hexaflexagons and pondering probability paradoxes.

I am sure it was reading Gardner that I first came across the peculiar “second child paradox”. While perhaps not strictly a paradox, it is at least a little counter-intuitive and goes something like this. Imagine you bump into an old friend you have not seen or heard from in years who tells you she has two children and one of them is a boy. What are the odds that she has two boys? Since the possibilities are Boy-Boy, Boy-Girl, Girl-Boy, the answer is 1/3. But if she had told you she has two children and the oldest is a boy, the odds that she has two boys are 1/2!

Of his science writings, my favourite is The Ambidextrous Universe (now in its third edition), which explores left and right “handedness”–the difference between an object and its mirror image–and its role in the physics of the universe. In exploring the notion of mirror symmetry, Gardner asks the strangely puzzling question why does a mirror reverse left and right but not up and down?

Gardner also gave me my first exposure to the debunking of pseudo-science. In 1952 he wrote “Fads & Fallacies in the Name of Science”, which takes on an eclectic mix of peculiar beliefs ranging from flat-earthers to UFO-logists, from bizarre beliefs about pyramids to ESP and from Forteans to medical quackery. But the chapter that has really stayed with me since reading Fads & Fallacies almost 30 years ago is the one on dianetics, the “science” behind Scientology.

In this chapter, Gardner describes the notion of an “engram”. According to adherents of dianetics, the unconscious mind has a habit of making recordings of painful experiences. These recordings, particularly those made as a child or even in utero, have a tendency to cause problems later in life. Of course, trained “auditors” can help identify and purge troublesome engrams. As Gardner notes, engrams seem to be susceptible to bad puns:

An auditor reported recently that a psychosomatic rash on the backside of a lady patient was caused by prenatal [engram] recordings of her mother’s frequent requests for aspirin. The literal reactive mind had been feeding this to her analytical mind in the form of “ass burn”.

As a skeptic, Gardner would look askance at anyone claiming to be able to predict the future, but it is a pity his own powers of prediction were not more accurate:

At the time of writing, the dianetics craze seems to have burned itself out as quickly as it caught fire, and Hubbard itself has become embroiled in a welter of personal troubles.

Sadly, Scientology is not only still around, it is probably stronger than it was back in the 1950s.

Science, mathematics and skepticism all continue to be very important to me, and I suspect that Martin had no small part to play in sowing their seeds in my mind many years ago. There are many others like me he has inspired and, along with his enormous catalogue of publications, that inspiration is a wonderful legacy.

I have a love/hate relationship with psychometric testing

A while ago, I had a bit of a rant in the post I Hate Personality Tests. Responding in this guest post, Maria Skarveli (who knows far more about psychology than I do) ponders personality testing phobia.

As a psychology student belonging to the faculty of health and behavioural sciences which also harbours biology, medical science and physiology, I was constantly hassled by my friends that were studying law, commerce and engineering and forever asking me “Can you read my mind?” or worse “Are you trying to analyse me?” as if I was Professor Xavier and I could distinguish mutants from humans. Of course I had to keep a straight face and stop myself from saying, “You’re an idiot, there you have it analysis complete” I just rolled my eyes and went with the flow. But deep down I was insulted. It was bad enough psychology had been branded as a “soft science”, which is apparently less intellectually stimulating than the “hard sciences” such as biology, physics and chemistry. But now the general view from all faculties was that psychology is akin to the paranormal, dare I say astrology!

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